Riding (country subdivision)

Etymology

The word riding is descended from late Old English *þriðing or *þriding (recorded only in Latin contexts or forms, e.g., trehing, treding, trithing, with Latin initial t here representing the Old English letter thorn). It came into Old English as a loanword from Old Norseþriðjungr, meaning a third part (especially of a county), cf. farthing. The modern form riding was the result of initial th being absorbed in the final th or t of the words north, south, east and west, by which it was normally preceded.

A common misconception holds that the term arose from some association between the size of the district and the distance that can be covered or encircled on horseback in a certain amount of time (cf. the Walking Purchase).

Scandinavia

In Iceland the third part of a thing which corresponded roughly to an English county was called þrithjungr. The island of Gotland and the Swedish province Närke were also divided into þrithjungar instead of hundreds.

Division is one of the three main methods used by gardeners to increase stocks of plants (the other two are seed-sowing and cuttings). Division is usually applied to mature perennial plants, but may also be used for shrubs with suckering roots, such as gaultheria, kerria and sarcococca. Annual and biennial plants do not lend themselves to this procedure, as their lifespan is too short.

Most perennials are best divided and replanted every few years to keep them healthy. They may also be divided in order to produce new plants. Those with woody crowns or fleshy roots need to be cut apart, while others can be prized apart using garden forks or hand forks. Each separate section must have both shoots and roots. Division can take place at almost any time of the year, but the best seasons are Autumn and Spring.

Division of the field

In heraldry, the field (background) of a shield can be divided into more than one area, or subdivision, of different tinctures, usually following the lines of one of the ordinaries and carrying its name (e.g. a shield divided in the shape of a chevron is said to be parted "per chevron"). Shields may be divided this way for differencing (to avoid conflict with otherwise similar coats of arms) or for purposes of marshalling (combining two or more coats of arms into one), or simply for style. The lines that divide a shield may not always be straight, and there is a system of terminology for describing patterned lines, which is also shared with the heraldic ordinaries. French heraldry takes a different approach in many cases from the one described in this article.

Division algorithm

A division algorithm is an algorithm which, given two integers N and D, computes their quotient and/or remainder, the result of division. Some are applied by hand, while others are employed by digital circuit designs and software.

Division algorithms fall into two main categories: slow division and fast division. Slow division algorithms produce one digit of the final quotient per iteration. Examples of slow division include restoring, non-performing restoring, non-restoring, and SRT division. Fast division methods start with a close approximation to the final quotient and produce twice as many digits of the final quotient on each iteration. Newton–Raphson and Goldschmidt fall into this category.

Discussion will refer to the form , where

N = Numerator (dividend)

D = Denominator (divisor)

is the input, and

Q = Quotient

R = Remainder

is the output.

Division by repeated subtraction

The simplest division algorithm, historically incorporated into a greatest common divisor algorithm presented in Euclid's Elements, Book VII, Proposition 1, finds the remainder given two positive integers using only subtractions and comparisons:

Riding (country subdivision)

Etymology

The word riding is descended from late Old English *þriðing or *þriding (recorded only in Latin contexts or forms, e.g., trehing, treding, trithing, with Latin initial t here representing the Old English letter thorn). It came into Old English as a loanword from Old Norseþriðjungr, meaning a third part (especially of a county), cf. farthing. The modern form riding was the result of initial th being absorbed in the final th or t of the words north, south, east and west, by which it was normally preceded.

A common misconception holds that the term arose from some association between the size of the district and the distance that can be covered or encircled on horseback in a certain amount of time (cf. the Walking Purchase).

Scandinavia

In Iceland the third part of a thing which corresponded roughly to an English county was called þrithjungr. The island of Gotland and the Swedish province Närke were also divided into þrithjungar instead of hundreds.

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